Erratum - BJID 15(5)

doi:10.1590/s1413-86702012000100025

Cited by 1 publication

(2 citation statements)

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“…Thus, the epidemic threshold is associated with this cluster becoming macroscopic, i.e., occupying a finite fraction of the system when L → ∞. Although we did not attempt to measure the basic reproduction number R 0 , i.e., the number of secondary infections that a single infected individual can generate before it dies or becomes cured [9,32,33], the outbreak cluster must be related to it [34]. Indeed, the presence of a percolating cluster above the threshold is the difference between an infection that dies out and the onset of an epidemic.…”

Section: Model and Observablesmentioning

confidence: 99%

“…A cornerstone of many theoretical studies in epidemiology is the SIR model and its many variants (see references [7][8][9][10][11] for recent reviews). Infectious agents (I) may either transmit the disease, with a given rate, to susceptible ones (S) through direct contact or, spontaneously, get removed (R) from the process by dying or recovering.…”

Section: Introductionmentioning

confidence: 99%

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A branching random-walk model of disease outbreaks and the percolation backbone

Oliveira¹,

Stariolo²,

Arenzon³

2022

J. Phys. A: Math. Theor.

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The size and shape of the region aﬀected by an outbreak is relevant to understand the dynamics of a disease and help to organize future actions to mitigate similar events. A simple extension of the SIR model is considered, where agents diﬀuse on a regular lattice and the disease may be transmitted when an infected and a susceptible agents are nearest neighbors. We study the geometric properties of both the connected cluster of sites visited by infected agents (outbreak cluster) and the set of clusters with sites that have not been visited. By changing the density of agents, our results show that there is a mixed-order (hybrid) transition where the region aﬀected by the disease is ﬁnite in one phase but percolates through the system beyond the threshold. Moreover, the outbreak cluster seems to have the same exponents of the backbone of the critical cluster of the ordinary percolation while the clusters with unvisited sites have a size distribution with a Fisher exponent τ < 2.

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